2009/09/21 by David Treumann · 2 citations
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #Algebraic structures and combinatorial models
paper · pdf · doi:10.1112/s0010437x09004229
Abstract For a Whitney stratification S of a space X (or, more generally, a topological stratification in the sense of Goresky and MacPherson) we introduce the notion of an S -constructible stack of categories on X . The motivating example is the stack of S -constructible perverse sheaves. We introduce a 2-category EP ≤2 ( X , S ), called the exit-path 2-category, which is a natural stratified version of the fundamental 2-groupoid. Our main result is that the 2-category of S -constructible stacks on X is equivalent to the 2-category of 2-functors 2Funct( EP ≤2 ( X , S ), Cat ) from the exit-path 2-category to the 2-category of small categories.